// need #include #include // data structure #include #include #include #include #include #include #include #include #include //#include #include #include #include #include // etc #include #include #include #include #include #include #include #include // input #define INIT std::ios::sync_with_stdio(false);std::cin.tie(0); #define VAR(type, ...)type __VA_ARGS__;MACRO_VAR_Scan(__VA_ARGS__); template void MACRO_VAR_Scan(T& t) { std::cin >> t; } templatevoid MACRO_VAR_Scan(First& first, Rest& ...rest) { std::cin >> first; MACRO_VAR_Scan(rest...); } #define VEC_ROW(type, n, ...)std::vector __VA_ARGS__;MACRO_VEC_ROW_Init(n, __VA_ARGS__); for(int w_=0; w_ void MACRO_VEC_ROW_Init(int n, T& t) { t.resize(n); } templatevoid MACRO_VEC_ROW_Init(int n, First& first, Rest& ...rest) { first.resize(n); MACRO_VEC_ROW_Init(n, rest...); } template void MACRO_VEC_ROW_Scan(int p, T& t) { std::cin >> t[p]; } templatevoid MACRO_VEC_ROW_Scan(int p, First& first, Rest& ...rest) { std::cin >> first[p]; MACRO_VEC_ROW_Scan(p, rest...); } #define VEC(type, c, n) std::vector c(n);for(auto& i:c)std::cin>>i; #define MAT(type, c, m, n) std::vector> c(m, std::vector(n));for(auto& R:c)for(auto& w:R)std::cin>>w; // output templatevoid MACRO_OUT(const T t) { std::cout << t; } templatevoid MACRO_OUT(const First first, const Rest...rest) { std::cout << first << " "; MACRO_OUT(rest...); } #define OUT(...) MACRO_OUT(__VA_ARGS__); #define FOUT(n, dist) std::cout<=(a);--w) #define REP(w, n) for(int w=0;w=0;--w) #define IN(a, x, b) (a<=x && x inline T CHMAX(T & a, const T b) { return a = (a < b) ? b : a; } template inline T CHMIN(T& a, const T b) { return a = (a > b) ? b : a; } // test template using V = std::vector; template using VV = V>; template std::ostream& operator<<(std::ostream& os, std::pair p) { os << "(" << p.first << ", " << p.second << ")"; return os; } // type/const #define int ll using ll = long long; using ull = unsigned long long; using ld = long double; using PAIR = std::pair; using PAIRLL = std::pair; constexpr int INFINT = (1 << 30) - 1; // 1.07x10^ 9 constexpr int INFINT_LIM = (1LL << 31) - 1; // 2.15x10^ 9 constexpr ll INFLL = 1LL << 60; // 1.15x10^18 constexpr ll INFLL_LIM = (1LL << 62) - 1 + (1LL << 62); // 9.22x10^18 constexpr double EPS = 1e-10; constexpr int MOD = 998244353; constexpr double PI = 3.141592653589793238462643383279; template void FILL(T(&a)[N], const T & val) { for (auto& x : a) x = val; } template void FILL(ARY(&a)[N][M], const T & val) { for (auto& b : a) FILL(b, val); } template void FILL(std::vector & a, const T & val) { for (auto& x : a) x = val; } template void FILL(std::vector> & a, const T & val) { for (auto& b : a) FILL(b, val); } // ------------>8------------------------------------->8------------ ll powMod(ll n, ll p, ll mod) { n %= mod; ll res = 1; while (p) { if (p & 1) res *= n, res %= mod; n *= n, n %= mod; p >>= 1; } return res; } int generator(int p) { std::vector fact; int phi = p - 1, n = phi; for (int i = 2; i * i <= n; ++i) if (n % i == 0) { fact.push_back(i); while (n % i == 0) n /= i; } if (n > 1) fact.push_back(n); for (int res = 2; res <= p; ++res) { bool ok = true; for (size_t i = 0; i < fact.size() && ok; ++i) ok &= powMod(res, phi / fact[i], p) != 1; if (ok) return res; } return -1; } // find x such that g^x == y (mod p) int BabyStepGiantStep(int p, int g, int y) { int m = std::ceil(std::sqrt(p)); std::unordered_map mp; mp.reserve(m); ll gj = 1; for (int j = 0; j < m; ++j) { mp[gj] = j; (gj *= g) %= p; } ll gm = powMod(g, p - 1 - m, p); ll ga = y; for (int i = 0; i < m; ++i) { auto it = mp.find(ga); if (it != mp.end()) return i * m + it->second; (ga *= gm) %= p; } return -1; } // Description: 整数列a[i],b[i]から列c[k]=sum{a[i]*b[k-i]}を生成する.任意modに対応.O(NlogN). namespace NTT { std::vector tmp; size_t sz = 1; inline int powMod(int n, int p, int m) { int res = 1; while (p) { if (p & 1) res = (ll)res * n % m; n = (ll)n * n % m; p >>= 1; } return (int)res; } inline int invMod(int n, int m) { return powMod(n, m - 2, m); } template struct NTTPart { static std::vector ntt(std::vector a, bool inv = false) { size_t mask = sz - 1; size_t p = 0; for (size_t i = sz >> 1; i >= 1; i >>= 1) { auto& cur = (p & 1) ? tmp : a; auto& nex = (p & 1) ? a : tmp; int e = powMod(PrimitiveRoot, (Mod - 1) / sz * i, Mod); if (inv) e = invMod(e, Mod); int w = 1; for (size_t j = 0; j < sz; j += i) { for (size_t k = 0; k < i; ++k) { nex[j + k] = (cur[((j << 1) & mask) + k] + (ll)w * cur[(((j << 1) + i) & mask) + k]) % Mod; } w = (ll)w * e % Mod; } ++p; } if (p & 1) std::swap(a, tmp); if (inv) { int invSz = invMod(sz, Mod); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * invSz % Mod; } return a; } static std::vector mul(std::vector a, std::vector b) { a = ntt(a); b = ntt(b); for (size_t i = 0; i < sz; ++i) a[i] = (ll)a[i] * b[i] % Mod; a = ntt(a, true); return a; } }; constexpr int M[] = { 998244353, 469762049, 167772161 }; constexpr int PR[] = { 3, 3, 3 }; constexpr int NTT_CONVOLUTION_TIME = 1; inline void garner(std::vector * c, int mod) { if (NTT_CONVOLUTION_TIME == 1) { for (auto& x : c[0]) x %= mod; } else if (NTT_CONVOLUTION_TIME == 2) { const int r01 = invMod(M[0], M[1]); for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)r01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0]) % mod; } } else if (NTT_CONVOLUTION_TIME == 3) { const int R01 = invMod(M[0], M[1]); const int R02 = invMod(M[0], M[2]); const int R12 = invMod(M[1], M[2]); const int M01 = (ll)M[0] * M[1] % mod; for (size_t i = 0; i < sz; ++i) { c[1][i] = (c[1][i] - c[0][i]) * (ll)R01 % M[1]; if (c[1][i] < 0) c[1][i] += M[1]; c[2][i] = ((c[2][i] - c[0][i]) * (ll)R02 % M[2] - c[1][i]) * R12 % M[2]; if (c[2][i] < 0) c[2][i] += M[2]; c[0][i] = (c[0][i] + (ll)c[1][i] * M[0] + (ll)c[2][i] * M01) % mod; } } } std::vector mul(std::vector a, std::vector b, int mod) { for (auto& x : a) x %= mod; for (auto& x : b) x %= mod; size_t m = a.size() + b.size() - 1; sz = 1; while (m > sz) sz <<= 1; tmp.resize(sz); a.resize(sz, 0); b.resize(sz, 0); std::vector c[NTT_CONVOLUTION_TIME]; if (NTT_CONVOLUTION_TIME >= 1) c[0] = NTTPart::mul(a, b); if (NTT_CONVOLUTION_TIME >= 2) c[1] = NTTPart::mul(a, b); if (NTT_CONVOLUTION_TIME >= 3) c[2] = NTTPart::mul(a, b); for (auto& v : c) v.resize(m); garner(c, mod); return c[0]; } }; // !!! CHECK NTT_CONVOLUTION_TIME !!! signed main() { INIT; VAR(int, p); VEC(int, a, p - 1); VEC(int, b, p - 1); a.insert(a.begin(), 0); b.insert(b.begin(), 0); int g = generator(p); V A(p - 1), B(p - 1); { int t = 1; REP(i, p - 1) { A[i] = a[t]; B[i] = b[t]; (t *= g) %= p; } } auto C = NTT::mul(A, B, MOD); { FOR(i, p - 1, C.size()) { (C[i % (p - 1)] += C[i]) %= MOD; C[i] = 0; } } V c(p, 0); { int t = 1; REP(i, p - 1) { c[t] = C[i]; (t *= g) %= p; } } FOR(i, 1, p) { OUT(c[i])SPBR(i, p) } return 0; }